1. Field of the Invention
The present invention relates for microlithographic technology and, particularly, to techniques implementing serifs for correcting severe optical proximity effects in microlithography.
2. Discussion of the Prior Art
Photolithography is the technology of reproducing patterns using light. As presently used in semiconductor industry, a photomask pattern for a desired circuit is transferred to a wafer through light exposure, development, etch, and resist strip, etc. As feature sizes on a circuit become smaller and smaller, the circuit shape on the wafer differs from the original mask pattern more and more. In particular, optical proximity effect phenomena such as corner rounding, line end foreshortening, iso-dense print bias, etc., are typically observed.
FIG. 1 illustrates a rectangular mask 10 and corresponding aerial image (after light exposure) of the final photoresist pattern 10' (indicated as broken lines) after further development, etch, and resist strip, etc. As shown in FIG. 1, the optical proximity effect of corner rounding is clearly exhibited as indicated at corners 12a-12d.
A simple geometric picture for understanding the optical proximity effects, such as the corner rounding, is additionally shown in FIG. 1. For definiteness, it is assumed that the clear region 10 of the mask portion 8 is inside the mask and serif boundaries.
For the case of incoherent light illumination (using either circular or rectangular aperture), the aerial image intensity at a point "E" is given by the convolution between the intensity kernel function and the transmitted light intensity around the point, and is proportional to the volume of a truncated cone-type 3D structure 15a (for the case of a square or rectangular aperture), and at a point "E'" by a truncated cone-type 3D structure 15b (for the case of a circular aperture), as shown in FIG. 1. Each whole cone-type structure 15a,15b represents the intensity kernel function on a respective 2D region centered at a point E (E') and has an effective range (radius) "r" which is basically the range of inference due to the optical proximity effects. In terms of the optical wavelength ".lambda." and the numerical aperture NA, the effective range "r" is of the order .lambda./NA. The truncation is done according to the actual light transmission around that point, which may be blocked by any opaque region 20 in the photomask, e.g., resulting in a half-rectangle region or a half-circle region. That is, as shown in FIG. 1, for an edge point E (when its distance to its nearest corner is larger than r), after truncation, the 2D area becomes rectangle represented by the half-square region 16a, i.e., its volume is half of whole volume under the intensity kernel function (i.e., half of whole volume of 3D cone-type structure for the case of a square or rectangular aperture). Similarly, for an edge point E', after truncation, the 2D area becomes a half-circle region 16b (for the case of a circular aperture). Moreover, as shown in FIG. 1, for a corner point "C," after truncation, its volume 18a is one quarter (1/4) of whole volume under the intensity kernel function (for the case of a square or rectangular aperture) and similarly, for a corner point C', the volume 18b is one quarter (1/4) of whole volume under the intensity kernel function (for the case of a circular aperture). Thus, I.sub.C =I.sub.E /2, with I.sub.C representing an illumination intensity at point C and I.sub.E representing an intensity at point E, independent of the range r and the form of the intensity kernel function. The aerial intensity contour line passing through the edge point E will not pass through the corner point C; rather, it passes through an inner point, resulting in the corner rounding effects.
For the case of coherent light illumination (with either circular or rectangular aperture), the aerial image intensity at a point is given by the square of the convolution between the amplitude kernel function and the actual transmitted light amplitude, and is proportional to the square of the volume of a truncated cone-type 3D structure. The whole cone-type structure represents the amplitude kernel function on a 2D region and is centered at that point and has a horizontal range r. In this instance, the truncation is also done according to the actual light transmission around that point, which may be blocked by any opaque region in the photomask. For an edge point E (when its distance to its nearest corner is larger than r), after truncation, its volume is half of whole volume under the amplitude kernel function (i.e., one-half of whole volume 3D cone-type structure). For a corner point C, after cut, its volume is one quarter (1/4) of whole volume under the amplitude kernel function. Thus, it is the case that I.sub.C =I.sub.E /4, also independent of the range r and the form of the amplitude kernel function. Here, 4 comes from the square of 2. The aerial intensity contour curve passing through the edge point E will not pass through the corner point C; rather, it passes through an inner point. Consequently, the corner rounding also exists for the coherent illumination.
For partially coherent light illumination, the corner rounding can be understood qualitatively: the light contribution to a corner point C' comes from within a quarter circle region of radius r (for circular aperture), e.g., at corner 12d (FIG. 1) which is less than the contribution of an edge point E coming from within a half-circle region of radius r; for a square aperture, it is from within a square region of length r, e.g., at corner 12b (FIG. 1) which is less than the contribution of an edge point E coming from within a rectangle of a size 2r.times.r. It is readily understood that a partial coherent illumination with large coherence factor ".sigma." may be approximated as an incoherent illumination. Likewise, a partial coherent illumination with small coherence factor ".sigma." may be treated as a coherent illumination.
Line end shortening can be understood similarly based on the geometric representations depicted in FIG. 1.
One of main reasons for optical proximity effects is light diffraction. Optical proximity effects coming from light diffraction may be overcome partly by using a shorter wavelength light source, and, with a projection system possessing a larger numerical aperture. In practice, the wavelength of an optical light source is typically fixed (365 nm, 248 nm, 193 nm, etc.) and there is a practical upper limit on numerical aperture. So other resolution enhancement methods, including the use of phase-shifting masks and masks with serifs, have been developed to correct optical proximity effects.
When optical proximity effects are not severe, both corner rounding and line end shortening can be corrected completely with the use of hanging serifs. This has been disclosed in detail in commonly-owned, co-pending U.S. patent application Ser. No. 09/167,948 entitled SERIF MASK DESIGN METHODOLOGY BASED ON ENHANCING HIGH SPATIAL FREQUENCY CONTRIBUTION FOR IMPROVED PRINTABILITY" the contents and drawings of which are wholly incorporated by reference as if fully set forth herein. U.S. Pat. No. 5,707,765 describes further techniques implementing serifs for correcting optical proximity effects in microlithographic circuits.
FIG. 2(a) depicts a serif design 28 in a photomask line end portion 21 for illumination by means including a square aperture and when the kernel function's range r is less than or equal to the pattern line width w, i.e., r.ltoreq.w. Within the intensity/amplitude kernel function representation at respective square regions 22a, . . . ,22d in FIG. 2(a), different truncations still lead to the same total volume of 3D cone structure resulting in I.sub.E =I.sub.C =I.sub.S =I.sub.N where I.sub.S is the illumination (aerial) intensity at point S and .sup.1 N is the illumination intensity at point N for both incoherent and coherent light illuminations. Thus, hanging square serifs 23a, . . . ,23d each of size r.times.r work ideally when r.ltoreq.w.
FIG. 2(b) similarly depicts a serif design 29 in a photomask line end portion 27 for illumination by means including a circular aperture and when the kernel function's radius r is not larger than the wire width "w", i.e., r.ltoreq.w. Within the intensity/amplitude kernel function representations at respective circular regions 24a, . . . ,24d in FIG. 2(b), different truncations still lead to the same total volume of 3D cone structure, i.e., I.sub.E =I.sub.C =I.sub.S =I.sub.N for both incoherent and coherent light illuminations. Thus, hanging quarter-circle serifs 25a, . . . ,25d of radius r serifs work ideally when r.ltoreq.w.
When optical proximity effects are severe (i.e., big corner rounding and large amount of foreshortening), the prior art serif mask designs (shown in FIGS. 2(a) and 2(b)) no longer work satisfactorily. These severe optical proximity effects occur when the kernel function's range r is larger than wire width w, which represents the typical feature size, i.e., patterned line width.
FIG. 3(a) depicts a serif design 30 in a photomask line end portion 31 for illumination by means including a square aperture when the kernel function's range r becomes larger than the line width w, i.e., r&gt;w. Now the masked areas (or unmasked areas) within 2D kernel representations 32a,32b in FIG. 3(a) are no longer equal, resulting in an unequal intensity relation I.sub.E .noteq.I.sub.C. Thus, hanging square serifs 33a,b, of size r.times.r no longer provides desired results on aerial image/resist pattern when r&lt;w.
FIG. 3(b) depicts a serif design 35 in a photomask line end portion 38 for illumination by means including a circular aperture when the kernel function's radius r becomes larger than the line width w, i.e., r&gt;w. Here, the mask areas (or unmasked areas) within 2D kernel representations 36a, 36b in FIG. 3(b) becomes unequal, resulting in an unequal intensity relation I.sub.E .noteq.I.sub.C. Consequently, hanging quarter-circle serifs 37a, 37b of radius r no longer provides desired results for optical proximity correction (OPC) when r&gt;w.
It would be highly desirable to provide a serif mask design for photolithographic mask that sufficiently corrects severe line end foreshortening and corner rounding effects for situations whereby the illumination kernel function's effective range (or radius) r is larger than the patterned line width w.